ζ-函数的特殊值的分母计算MOD p摩尔谱的ku -局部同伦群

IF 0.7 4区数学 Q2 MATHEMATICS

Rocky Mountain Journal of Mathematics Pub Date : 2023-03-16 DOI:10.1216/rmj.2023.53.915

A. Salch

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引用次数: 3

摘要

在本文中，我们证明了对于每一个奇素数$p$摩尔谱的$KU$-局部同伦群的阶数等于全实数域的Dedekind ζ函数的某些商的特殊值的分母。有了这个观察结果，我们给出了这些数域的利奥波德猜想的一个可爱的拓扑证明，通过证明它是$KU$-局部稳定同伦群的周期性的结果。

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DENOMINATORS OF SPECIAL VALUES OF ζ-FUNCTIONS COUNT KU-LOCAL HOMOTOPY GROUPS OF MOD p MOORE SPECTRA

In this note, for each odd prime $p$, we show that the orders of the $KU$-local homotopy groups of the mod $p$ Moore spectrum are equal to denominators of special values of certain quotients of Dedekind zeta-functions of totally real number fields. With this observation in hand, we give a cute topological proof of the Leopoldt conjecture for those number fields, by showing that it is a consequence of periodicity properties of $KU$-local stable homotopy groups.

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来源期刊

Rocky Mountain Journal of Mathematics 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

7.5 months

期刊介绍： Rocky Mountain Journal of Mathematics publishes both research and expository articles in mathematics, and particularly invites well-written survey articles. The Rocky Mountain Journal of Mathematics endeavors to publish significant research papers and substantial expository/survey papers in a broad range of theoretical and applied areas of mathematics. For this reason the editorial board is broadly based and submissions are accepted in most areas of mathematics. In addition, the journal publishes specialized conference proceedings.